Landscape Cartography: A Coarse Survey of Gauge Group Rank and Stabilization of the Proton

TL;DR

This paper surveys string theory vacua to analyze gauge group ranks, their distribution, and implications for proton stability, providing formulas and insights into landscape averages and their limitations.

Contribution

It derives a simple formula for average gauge group rank on the string landscape and explores its implications for proton stability and vacuum distributions.

Findings

Average gauge group rank can be estimated with a derived formula.

Small cosmological constant slightly increases gauge group rank.

Vacuum counts with additional gauge groups impact proton stability considerations.

Abstract

The landscape of string/M theory is surveyed over a large class of type $IIB$ flux compactification vacua. We derive a simple formula for the average size of the gauge group rank on the landscape under assumptions that we clearly state. We also compute the rank under the restriction of small cosmological constant, and find a slight increase. We discuss how this calculation could impact proton stability by computing the suppression factor for the number of vacua with additional gauge group rank that could be used to protect the proton. Finally, we present our views on the utility and limitations of landscape averages, especially in the context of this analysis.